is real-valued and satisfies \(J^{2}=-\mathbb {I}\) , so it defines a complex structure
in each tangent space, and the space of complex (Hermitian) structures at any point is again parametrized by \(\mathbb {CP}^{1}\) .
In this way we recover the Riemannian results for almost-complex structures given in [1]} and
[2]} (see eq. (9.1.20) in the first reference and page 429 in the second).

